The invention relates to medical guidewires for narrow passages of a body, and particularly guidewires that are designed to cross an occlusion of a duct or vessel, such as a coronary artery. A physician introduces the distal end of the guidewire into the body, e.g., via a puncture, and manipulates the flexible tip of the guidewire to enter the desired passageway and follow its convolutions to a treatment site. A dilatation catheter or other medical device may then be advanced over the guidewire to the site.